3a6 HISTORY OF WESTERN EDUCATION attained by making instruction follow the order of the mind's growth. This is obvious in the precedence of speaking to reading, and of drawing to writing. He would make it the rule for all instruction. The right order of learning is the psychological order which proceeds by gradual steps from the near to the remote, from the simple to the complex. Pestalozzi elaborates this idea of natural beginnings and sequence of learning in what he calls the A B C of Anschauung. There are certain general ideas which must become the personal possession of the child if he is to attain to intellectual manhood, notably the ideas of number, form und name. As they stand in adult experience they are far above the level of the child. The teacher must bring them down to their elements in sense experiences (Anschauungen) in the same way as language has been analysed into words and words into letters, like ABC; and he must gradually form the child's mind by teaching him these essential facts, first in their detachment and subsequently in all their relations. In the study of number, the foundations are laid on a sure knowledge of the elementary relations of measurable quantities. " Arithmetic arises entirely from simply putting together and separating several units. Its basis is es- sentially this: * One and one is two. One from two leaves one.* Any number whatever is only an abbreviation of processes which are fundamental in all numeration."* The right beginning in arithmetic is made when the child learns to count the things around him—the number of steps across the room, the number of plies in the thread he is weaving, etc.—and comes to know in this way what each single number means. Out of this develops addition, and it is only a further stage in the same process to multiplication, subtraction and division. Once these operations are understood in this direct way, the child is ready for the counting tables devised by Pestalozzi in which strokes take the place of objects. In the study of form, the elements are certain lines and angles which are the component parts of even the most complex figures. In the study of names (that is, of language), the fundamental units are the elementary sounds which in their combinations . constitute speech. From the articulation of these the child passes successively to the reading of syllables, words, sentences. At each stage there is a great variety of exercises in langauge, * How Gertrude Teaches Her Children, viii.